SOme of the things you mention just make no sense as an upgrade... Why bother switching to 31.8mm stem clamp? I don't think there has been an 'improvement' to bikes in a long time that makes less of an improvement to how the bike rides or feels. If you balk at the cost of an Alfine integrated shifter then how comfortable are you with the $600 hub without shifters?

There is no reason why your 25 year old bike cannot ride as fast or as smoothly as a brand new bike, simply with a little TLC.

Trying to install brifters will mean changing almost every part of the drivetrain - hub, cogs, derailleur, shifters, chain, likely cranks and bottom bracket...nothing new will work with your old stuff. Plus you will need to re-space the frame to make it fit. But that doesn't mean your stuff is bad - just old. Get some friction bar-end shifters (like Suntour bar-cons) and ride that bike 'till the wheels fall off... then re-attach the wheels and ride some more.

If you are determined to go through with an 'upgrade,' consider buying a cheap 'doner bike' and swapping all compatible parts. Although with an old French bike you might find many parts will not simply swap over.
Full disclosure: I ride a 1976 steel 10-speed frame (CCM Torino 76) with an ALfine 8 speed hub... but my bike was not complete when I got it, otherwise I would have left it alone.